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Clock Problems

Asad Aziz

Competitive Maths Series

Clock Problems

  1. A clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?

(a) 144º                (b) 150º

(c) 180º                 (d) 210º

  1. The reflex angle between the hands of a clock at 10:25 is:

(a) 180º                (b) 192½º

(c) 197½ º             (d) 200º

  1. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

(a) 120º                (b) 145º

(c) 150º                (d) 155º

  1. A watch which gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day, when the watch indicated quarter past 4 o’clock, the true time is:

(a) 4:00 pm          (b) 4:30 pm

(c) 5:00 pm          (d) 5:15 pm

  1. The angle between the minute hand and the hour hand of a clock when the time is 4:20, is:

(a) 5º                     (b) 10º

(c) 15º                   (d) 20º

  1. At what angle the hands of a clock are inclined at 15 minutes past 5?

(a) 58½º                (b) 64º

(c) 66º                   (d) 67½º

  1. At 3:40, the hour hand and the minute hand of a clock form an angle of:

(a) 120°                (b) 130°

(c) 135°                (d) 140°

  1. How many times are the hands of a clock at right angle in a day?

(a) 22                    (b) 24

(c) 44                    (d) 48

  1. The angle between the minute hand and the hour hand of a clock when the time is 8:30, is:

(a) 60                    (b) 70

(c) 75                    (d) 105

  1. How many times in a day, are the hands of a clock in straight line but opposite in direction?

(a) 20                    (b) 22

(c) 36                    (d) 44

  1. How many times do the hands of a clock coincide in a day?

(a) 16                    (b) 18

(c) 20                    (d) 22

  1. A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min 48 sec fast at 2 pm on the following Monday. When was it correct?

(a) 2 pm on Tuesday

(b) 2 pm on Wednesday

(c) 3 pm on Thursday

(d) 1 pm on Friday

  1. A watch loses 5 minutes every hour and was set right at 8 AM on a Monday. When will it show the correct time again?

(a) 8:00 am on Sunday     

(b) 11:30 am on Sunday

(c) 8:00 am on Monday

(d) 9:30 am on Monday

  1. A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?

(a) 11:48 am        (b) 12:14 pm

(c) 12:34 pm        (d) 12:48 pm

  1. An accurate clock shows 8 o’clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?

(a) 60º                   (b) 90º

(c) 150º                (d) 180º

 A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?

(a) 10 pm              (b) 11 pm

(c) 11:30 pm        (d) 12:15 pm

  1. The reflex angle between the hands of a clock at 10.25 is:

(a) 80½                (b) 160½

(c) 197½               (d) 214½

  1. At what angle the hands of a clock are inclined at 15 minutes past 5?

(a) 57.5º                              (b) 62.5º

(c) 67.5º                (d) 72.5º

  1. The angle between the minute hand and the hour hand of a clock when the time is 8:30 is:

(a) 45º                   (b) 60º

(c) 75º                   (d) 90º

  1. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o’clock, the true time is:

(a) 3:00pm           (b) 3:30pm

(c) 4:00pm            (d) 4:30pm

Clock Important Formulas

  1. In 60 minutes, the minute hand gains 55 minutes on the hour hand
  2. In every hour, both the hands coincide once.
  3. The hands are in the same straight line when they are coincident or opposite to each other.
  4. When the two hands are at right angles, they are 15 minute spaces apart
  5. When the hands are in opposite directions, they are 30 minute spaces apart
  6. Angle traced by hour hand in 12 hrs = 360°.
  7. Angle traced by minute hand in 60 min. = 360°.
  8. Too Fast and Too Slow: If a watch or a clock indicates 8.15, when the correct time, 8 is said to be 15 minutes too fast.
  9. On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

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